Model each problem as an equation, and then match to its solution.

Answer:

r > 17

Step-by-step explanation:

r -7> 10

Add 7 to each side

r-7+7 > 10+7

r > 17

ANSWER

(-2,-1)

(3,14)

EXPLANATION

The given system is

[tex]y = {x}^{2} + 2x - 1[/tex]

[tex] y - 3x = 5[/tex]

or

[tex]y = 3x + 5[/tex]

Equate both of them:

[tex]{x}^{2} + 2x - 1 = 3x + 5[/tex]

This implies that,

[tex]{x}^{2} - x - 6 = 0[/tex]

[tex](x - 3)(x + 2) = 0[/tex]

x=-2 or x=3

When x=-2, y=y=3(-2)+5=-1

(-2,-1) is a solution.

When x=3 , y=3(3)+5=14

(3,14) is also a solution.

Answer: $47,880

Step-by-step explanation:

APEX

Answer:

Leif makes $47880 in interest.

Step-by-step explanation:

Given: Interest rate (r) = 26,100%

r = [tex]\frac{26600}{100} = 266[/tex]

Principle (p) = $180

time (t) = 1

Now we have to find the simple interest. The simple interest formula is  I=prt

Plugging in the given values, we get

I = 180×266×1

I = $47880

So Leif makes $47880 in interest.

What are the choices

Answer: 8 I think!

Hope it helps

Answer:

[tex](2-5i)(p+q)(i)=29i[/tex]

Step-by-step explanation:

We have the product of 2 complex numbers

[tex](2-5i)(p+q)(i)[/tex]

We know that:

[tex]p=2\\\\q=5i[/tex]

Then we substitute these values in the expression

[tex](2-5i)((2)+(5i))(i)[/tex]

[tex](2-5i)(2+5i)(i)[/tex]

The product of a complex number [tex]a + bi[/tex] by its conjugate [tex]a-bi[/tex] is always equal to:

[tex]a ^ 2 - (bi) ^ 2[/tex]

Then

[tex](2-5i)(2+5i)(i)=(2^2-5^2i^2)(i)[/tex]

Remember that:

[tex]i=\sqrt{-1}\\\\i^2 = -1[/tex]

So

[tex](2^2-5^2i^2)(i)= (4 - 25(-1))(i)\\\\(4 - 25(-1))(i) = (4+25)i=29i[/tex]

Finally

[tex](2-5i)(p+q)(i)=29i[/tex]

Answer:

29i

Step-by-step explanation:

Edge Verified

Answer:

B) B(2,-3) and C(-2,3)

Step-by-step explanation:

The given point A, has coordinates (-2,-3).

When point A(-2,-3) is reflected over the y-axis to obtain point B, then the coordinates of B is obtained by negating the x-coordinate of A.

Therefore B will have coordinates (2,-3).

 When point A(-2,-3) is reflected over the x-axis to obtain point C, then the coordinates of C is obtained by negating the y-coordinate of A.

Hence the coordinates of C are (-2,3)

Answer:

Problem 12 is 112° and problem 13 is 68°

Step-by-step explanation:

Angles EPF and DPG are vertical angles; therefore, they are congruent.  That means, algebraically, that

4x + 48 = 7x

Solving for x:

48 = 3x  and  x = 16

Now that we know the value of x we can sub it back into the expression for the angle:

4(16) + 48 = 112.

For problem 13, angles DPE and EPF are supplementary, so that means that they add up to equal 180 degrees.  Therefore, 180 - 112 = 68 degrees.

The car, which depreciates at an annual rate of 1.4%, will be worth approximately £2590.34 in 5 years.

This is a problem related to depreciation, which is a concept in finance and economics. In this case, the car depreciates at a rate of 1.4% per year. This means that each year, the value of the car decreases by 1.4% of its value at the start of that year. This is an example of exponential decay.

To calculate the car's value after 5 years, we raise the depreciation rate (99.6%, or 0.996 in decimal form because the value decreases) to the power of 5, and then multiply it by the initial price of the car, £2700.

That is, Car Value = £2700 * (0.996)^5 = £2590.34

So, the car will be worth approximately £2590.34 in 5 years to the nearest penny.

https://brainly.com/question/17827672

#SPJ

Answer:

  about 0.53

Step-by-step explanation:

54% of the insured, or .54×900 = 486 individuals are males. That leaves 900-486 = 414 that are females. 43% of those, or .43×414 = 178 are over 25, so the remainder of the 395 who are over 25 are male.

Since 395 -178 = 217 of the males are over 25, there are 486 -217 = 269 who are under 25. Then the fraction of insureds who are under 25 that are male is ...

  269/(900 -395) = 269/505 ≈ 0.53

_____

It can be useful to make a 2-way table from the given information.

Final answer:

Using the provided data, the probability that a person under 25 years old selected randomly is male is calculated by dividing the number of males under 25 (found by subtraction from total males and males over 25) by the total number of individuals under 25.

Explanation:

The question asks us to calculate the probability that a person under 25 years old, selected randomly from a group of insured individuals, is male. To find this, we need to use the given data:

Total insured individuals: 900

Percentage of males: 54%

Individuals over 25 years old: 395

Probability that a randomly selected female is over 25: 0.43

To calculate the number of males and females, we take 54% of 900 to get the total males, which is 486. Since there are 900 insured individuals in total, the number of females would be 900 - 486 = 414. The number of females over 25 years old is 414 * 0.43 = 178.02, which we can round to 178.

Since there are 395 individuals over 25 years old in total and 178 of them are female, 395 - 178 gives us 217 males over 25 years old. Now, we need to find the number of individuals under 25 years old. There are 900 - 395 = 505 individuals under 25.

The probability that a randomly selected person under 25 is male can be found by dividing the number of males under 25 by the total number of people under 25. The number of males under 25 is the total number of males minus males over 25, which is 486 - 217 = 269. Therefore, the probability is 269 / 505.

Answer:

C. 531 would be your answer.

Answer: 531

Step-by-step explanation: 21 • 18 = 378 and 17 • 9 = 153. And those together and you get 531 as yours answer!

Standard form for linear equations is in the form ax + by = c. Thus, 2x + 4y = -3 is already in standard form.

Answer:

It is already in standard form

Step-by-step explanation:

Standard form is ax+by=c

2x=ax

4y=by

-3=c

Nothing needs to be changed

Answer:

16

Step-by-step explanation:

96 marbles = Box

Let's call blue marbles " 5 x " and red marbles " x "

So now an equation is setup ⇒

→ 5 x + x = 96

( Simplify )

→ 6 x = 96

( Divide by 6 from both sides to isolate x )

→ x = 16

red marbles " x " so x = 16

You would use the following equation:

96 = 5x + x

There is a total of 96 marbles. The right side of the equation represents how many blue marbles are in the box. X is red marbles in the box, since we know that red marbles is 5 times x

Add the common variables:

96 = 5x + x

96 = 6x

To solve for red marbles isolate x. To do this divide 6 to both sides. Division is the opposite of multiplication and will cancel 6 from the right side and bring it to the left

96 ÷ 6 = 6x ÷ 6

16 = x

You have 16 marbles in the box

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

[tex]\boxed{3x - y = 5}}[/tex]

Step-by-step explanation:

The coordinates of the two points are (4, 7) and (3, 4).

(a) Calculate the slope of the line

[tex]\begin{array}{rcl}m & = & \dfrac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\&= & \dfrac{7 - 4}{4 - 3}\\\\& = & \dfrac{3}{1}\\\\ & = &3\\\end{array}[/tex]

(b) Calculate the y-intercept

[tex]\begin{array}{rcl}y & = & mx + b\\7 & = & 3 \times 4 + b\\7 & = & 12 + b\\b & = & -5\\\end{array}[/tex]

(c) Write the equation for the line

y = 3x - 5

This is the point-slope form of the equation.

(d) Convert to standard form

[tex]\begin{array}{rcl}y & = & 3x - 5\\-3x + y & = & -5\\3x - y & = & -5\\\end{array}\\\text{The standard form of the equation is }\boxed{\mathbf{3x- y = -5}}[/tex]

The equation of the line in the form of Ax + By = C is 3x - y = 7.

Given that,

The equation of the line in the form Ax +By = C,

Which passes through the points (4, 3) and (3,4).

We have to determine,

The equation of the line.

According to the question,

The equation of the line in the form Ax +By = C,

The co-ordinate passes through the points (4, 3) and (3,4).

To determine the equation of the line following all the steps given below.

                   [tex]m = \dfrac{y_2-y_1}{x_2-x_2}\\\\m = \dfrac{4-7}{3-4}\\\\m = \dfrac{-3}{-1}\\\\m = 3[/tex]

                The slope of the line is 3.

                    [tex]y = mx + c\\\\7= 3 \times 4 + c\\\\7 = 12+ c\\\\c = 7-12\\\\c = -5[/tex]

                    The y-intercept of the line is -7.

                     [tex]y = mx + c \\\\y = 3x-7[/tex]

                    [tex]y = 3x - 7\\\\3x -y = 7[/tex]

Hence, The equation of the line in the form of Ax + By = C is 3x - y = 7.

To know more about Linear equations click the link given below.

https://brainly.com/question/15874858

Answer:

The CORRECT answer is 97.4 in ^2

Step-by-step explanation:

Usatestprep , the other answer is wrong trust me.

is noteworthy that the leading term has a negative coefficient, meaning this parabola is opening downwards like a "camel hump", so it reaches a maximum point and then goes back down, and of course the maximum point is at its vertex.

[tex]\bf \textit{vertex of a vertical parabola, using coefficients} \\\\ H(x)=\stackrel{\stackrel{a}{\downarrow }}{-\frac{1}{2}}x^2\stackrel{\stackrel{b}{\downarrow }}{+4}x\stackrel{\stackrel{c}{\downarrow }}{-5} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right) \\\\\\ \left(-\cfrac{4}{2\left( -\frac{1}{2} \right)}~~,~~-5-\cfrac{4^2}{4\left( -\frac{1}{2} \right)} \right)\implies \left( 4~,~-5+\cfrac{16}{2} \right)\implies (4~~,~~3)[/tex]

Answer:

(4, -3)

Step-by-step explanation:

I'm assuming that you meant  H(x) = -(1/2)x^2 + 4x - 5.  Here, the coefficients of this quadratic are a = -1/2, b = 4 and c = -5.

The axis of symmetry is x = -b/(2a).  This axis goes through the vertex.  Here the axis of symmetry is  x = -(4) / [ 2(-1/2) ], or x = 4.

Evaluating H(x) at x = 4 gives us the y value of the vertex.  It is:

H(4) = (-1/2)(4)^2 + 4(4) - 5, or H(4) = -8 + 16 - 5, or 3.

We know that this function must have a max because a is - and therefore the graph opens down.

The vertex and the maximum is (4, 3).

Answer:

  (c) 16/9·π²·r⁶

Step-by-step explanation:

The water displaced is equivalent to the volume of the sphere, given as

  V = (4/3)π·r³

The product of two identical displaced volumes will be ...

  V² = ((4/3)π·r³)² = (4/3)²·π²·r⁶

  = 16/9·π²·r⁶ . . . . . . matches choice (c)

Answer:

c. 3 + 2 cosθ

Step-by-step explanation:

a = 3, b = 2

Since a > b, 1 < [tex]\frac{3}{2}[/tex] <2

we get a dimpled limacon.

Answer:

Correct option is C ) [tex]r=3+2\,cos\theta[/tex]

Step-by-step explanation:

Limacons are polar functions of the type:

[tex]r=a\pm\,b\,cos\theta[/tex]

[tex]r=a\pm\,b\,sin\theta[/tex]

Where [tex]|\frac{a}{b}|<1\,or\,1<|\frac{a}{b}|<2\,or\,|\frac{a}{b}|$\geq$2[/tex]

In provided options part (a) and (d) constants 'a' and 'b' does not satisfied the condition,

in part (b) and (c) both satisfies the condition but in part (b) we get loop  inside the sketch.

so,  [tex]r=3+2\,cos\theta[/tex] satisfies the condition of graph.

hence correct option is c )  [tex]r=3+2\,cos\theta[/tex] .

Answer:

g(x) = x^2 + 4x + 4

Step-by-step explanation:

In translation of functions, adding a constant to the domain values (x) of a function will move the graph to the left, while subtracting from the input of the function will move the graph to the right.

Given the function;

f(x) = x2 - 6x + 9

a shift 5 units to the left implies that we shall be adding the constant 5 to the x values of the function;

g(x) = f(x+5)

g(x) = (x+5)^2 - 6(x+5) + 9

g(x) = x^2 + 10x + 25 - 6x -30 + 9

g(x) = x^2 + 4x + 4

Answer:

A. y=1-2x

Step-by-step explanation:

if to substitute the values of 'x'=1; 2; 3; 4 into the equations, only the 'A' is correct.

Answer:

A. y=1-2x

Step-by-step explanation:

if to substitute the values of 'x'=1; 2; 3; 4 into the equations, only the 'A' is correct.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Proof:

_____

Proof is always in the eye of the beholder, and the details depend on the supporting theorems and postulates you're allowed to invoke. The basic idea is that you have cut a vertex angle in half twice, and you're trying to show that the smallest part to the rest of it has the ratio 1 : 3.

Answer:

3.8 meters

Step-by-step explanation:

In order to find the circumference for a circle, we use the formula π(radius)²

The circumference give is 45.84 and the π given is 3.14

All we have to do is to just substitute them.

45.84 = 3.14(radius)²

45.84 / 3.14 = radius²

14.6 = radius²

radius = √14.6

radius = 3.82 ≅ 3.8

Answer:

approx. 7.3 m

Step-by-step explanation:

The formula for the circumference of a circle is  s = r·Ф, where r is the radius and Ф is the central angle in radians.

Here C = 45.84 m = 2π·r.  Solving for the radius, r, we get:

       45.84 m

r = --------------- = 7.299 m, or approx. 7.3 m.

          2(3.14)

Answer:

  {-12, -11}

Step-by-step explanation:

Let x represent the smaller of the two integers. The problem statement tells us ...

  x +1 = (1/3)x -7

  (2/3)x = -8 . . . . . . subtract 1/3x +1

  x = -12 . . . . . . . . . multiply by 3/2

The integers are -12 and -11.

Final answer:

To find two consecutive integers where the greater is 7 less than one-third the smaller, we defined the smaller integer as x and set up an equation: x + 1 = (x/3) - 7. Solving through algebraic operations, we found the integers to be -12 and -11.

Explanation:

To solve for two consecutive integers where the greater is 7 less than one-third the smaller integer, let us denote the smaller integer as x and the greater as x + 1. According to the problem, the greater integer (x + 1) is 7 less than one-third the smaller integer (x/3). Thus, we can set up the equation:

x + 1 = (x/3) - 7

To solve for x, we perform the following steps:

Multiply all terms by 3 to eliminate the fraction: 3(x + 1) = x - 21.

Distribute the 3: 3x + 3 = x - 21.

Combine like terms: 2x = -24.

Divide both sides by 2: x = -12.

Now that we have found the smaller integer to be -12, the greater integer is just one more, so it is -11.

Therefore, the two consecutive integers are -12 and -11.

[tex]\bf 2m^2+3=m\implies 2m^2-m+3=0 \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf \qquad \qquad \qquad \textit{discriminant of a quadratic} \\\\\\ \stackrel{\stackrel{a}{\downarrow }}{2}m^2\stackrel{\stackrel{b}{\downarrow }}{-1}m\stackrel{\stackrel{c}{\downarrow }}{+3} ~~~~~~~~ \stackrel{discriminant}{b^2-4ac}= \begin{cases} 0&\textit{one solution}\\ positive&\textit{two solutions}\\ negative&\textit{no solution}\qquad \checkmark\\ &\textit{two \underline{non-real roots}} \end{cases} \\\\\\ (-1)^2-4(2)(3)\implies 1-24\implies -23[/tex]

For this case we have that by definition, the Greatest Common Factor or GFC, of two or more integers is the largest integer that divides them without leaving a residue.

So:

We look for the factors of both numbers:

8: 1, 2, 4, 8

40: 1, 2, 4, 5, 8, 10, 20

It is observed that 8 is common.

So, the GFC of 8x and 40 is 8

Answer:

8

ANSWER

15 gallons

EXPLANATION

The equation that models the situation is

[tex]g(m) = 15 - \frac{m}{32} [/tex]

When the tank was full the man did not cover any mile.

To find the the number of gallons of gases Vera's tank holds, we substitute m=0 into the equation to get,

[tex]g(0) = 15 - \frac{0}{32} = 15[/tex]

Therefore the correct answer is is option A 15 gallons

Final answer:

When Vera's tank is full, it holds 15 gallons of gas. This is found by setting the miles driven to zero in the equation g = 15 - (m/32).

Explanation:

To determine how many gallons of gas Vera's tank holds when full, we need to set m, the number of miles driven, to zero in the given equation g = 15 - (m/32). This is because we are interested in the initial amount of gas before any driving occurs.

Plugging m = 0 into the equation gives us:

g = 15 - (0/32)

g = 15

Therefore, when full, Vera's tank holds 15 gallons of gas. Among the provided options, the correct answer is 15 gallons.

Answer:

Option B.

Step-by-step explanation:

Two events are said to be independent of each other, if the probability of one event ocurrin in not way affects the probability of the other event occurring.

The interception of two independent events P(A ∩ B) = P(A) × P(B), where:

P(A) = 0.70

P(B) = 0.20

P(A ∩ B) = P(A) × P(B) = 0.70x0.20 = 0.14

The two events are independent if the probability of buying Bread AND cheese equals: 0.14, which is Option B.

Answer:

B

Step-by-step explanation:

Answer:

  y = x+6

Step-by-step explanation:

You can find an equation by using the 2-point form of the equation for a line:

  y = (y2 -y1)/(x2 -x1)·(x -x1) +y1

Filling in the given values, we have ...

  y = (9 -5)/(3 -(-1))·(x -(-1)) +5

  y = (4/4)(x +1) +5 . . . . simplifying a bit

  y = x +6

Answer:

b. (w -4)(w +1)

Step-by-step explanation:

The problem statement asks for an expression for the rug area "based on the width of the room." Looking at the answer choices, we see that the variable "w" is used to represent the width of the room.

The dimensions of the room are its width (w) and its length, which is 5 more than its width (w+5).

The dimensions of the rug are 4 ft smaller in each direction (2 ft on each side), so the width of the rug is w-4, and the length of the rug is w+5-4 = w+1.

The area of the rug is the product of its width and length, so is ...

(w-4)(w+1) . . . . . matches selection B

Answer:

Actually, what you said you have so far is not correct.  The 2 correct answers are the 1st one (x + y = 15) and the 5th one (15x + 10y > 180)

Step-by-step explanation:

If tutoring French is x hours and scooping ice cream is y hours and he is going to work 15 hours for sure doing both, then we can add them together to get that x hours + y hours = 15 hours, or put simply:  x + y = 15.

Now we are going to throw in the added fun of the money he makes doing each.  The thing to realize here is that we can only add like terms.  So looking at the equation above, we have x hours of tutoring and y hours of scooping, so if we want to add them, we will add those number of hours together to get the total number of hours he worked, which we know to be 15.  The same goes for money.  If we add money earned from tutoring to money earned from scooping, we need that to be greater than the money he wants to earn which is 180 at least.  Because he wants to earn MORE than $180. we use the ">" sign.  Since he earns $15 an hour tutoring, that expression is $15x; since he earns $10 an hour scooping, that expression is $10y.  Now add them together (and you CAN because they are both expressions relating dollars to dollars) and set the sum > $180:

$15x + $10y > $180.  That's why your answer is not correct.  Use mine (with the understanding that you care about why yours is wrong and mine is correct) and you'll be fine.

Answer:

  200 ft²

Step-by-step explanation:

Each face is an isosceles right triangle with a hypotenuse of length 10 ft. The area of each of those triangles is

  A = 1/4·h² . . . . where the h in this formula is the hypotenuse length

So, the area of the four faces (the lateral area of the pyramid is 4 times this, or ...

  A = 4·1/4·(10 ft)² = 100 ft²

Of course, the base area is simply the area of the square base, the square of its side length:

  A = (10 ft)² = 100 ft²

So, the total area is the sum of the lateral area and the base area:

  total area = 100 ft² +100 ft² = 200 ft²

_____

If you think about this for a little bit, you will realize the pyramid must have zero height. That is, the slant height of a face is exactly the same as the distance from the center of an edge to the center of the base. "Not drawn to scale" is a good description.

Answer:

200 [tex]ft^{2}[/tex]

Step-by-step explanation: